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Quiz about The Mysteries of Manyfaced Mathematical Parrots
Quiz about The Mysteries of Manyfaced Mathematical Parrots

The Mysteries of Many-faced Mathematical Parrots Quiz


How much do you know about those (mostly regular) solid POLYhedra?

A multiple-choice quiz by Flamis. Estimated time: 4 mins.
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Author
Flamis
Time
4 mins
Type
Multiple Choice
Quiz #
327,919
Updated
Jul 23 22
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
384
- -
Question 1 of 10
1. First, you need to know what a polyhedron is. So, which of these is the classic definition of a polyhedron? Hint


Question 2 of 10
2. Which part of a polyhedron is called a vertex? Hint


Question 3 of 10
3. The simplest regular polyhedron has just four faces. What is it called? Hint


Question 4 of 10
4. What shape are the faces of a regular tetrahedron? Hint


Question 5 of 10
5. The most familiar polyhedron is the regular hexahedron. What is the more common name of the regular hexahedron? Hint


Question 6 of 10
6. The next regular polyhedron has eight triangular faces and twelve edges. What is it called? Hint


Question 7 of 10
7. Mathematicians call the ten-sided die a pentagonal trapezohedron, which might be considered a bit strange because its faces are not pentagons. What shape are the ten faces of the pentagonal trapezohedron? Hint


Question 8 of 10
8. The dodecahedron has twelve faces. What shape are the faces of the regular dodecahedron? Hint


Question 9 of 10
9. The last of the regular polyhedra has twenty faces, all of them equilateral triangles. What is it called? Hint


Question 10 of 10
10. There are in fact only five convex polyhedra that are also regular, all their faces being regular polygons of the same size. They are named for a Greek philosopher. What are they called? Hint



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Quiz Answer Key and Fun Facts
1. First, you need to know what a polyhedron is. So, which of these is the classic definition of a polyhedron?

Answer: Any three-dimensional geometric solid with flat sides and straight edges

The word comes from the Greek "poly" = many, and "hedron" = face or base. Modern mathematicians, being the complicated individuals that they are, find this definition imprecise, and not at all satisfactory - but it's the one your maths teacher would probably have taught you.
2. Which part of a polyhedron is called a vertex?

Answer: Corner

If you're talking about more than one corner, they're called vertices. The word "vertex" comes from a Latin word meaning "turning point".
3. The simplest regular polyhedron has just four faces. What is it called?

Answer: Tetrahedron

If you've ever played with polyhedral dice, you'll know the tetrahedron as the d4, the four-sided die (also known as the caltrop - even those who haven't played will probably wince at the thought of accidentally standing on a little pyramid made of hard plastic resin!) The caltrop is in reality a nasty little device composed of four spikes pointing outwards into the corners of a tetrahedron. This meant that when a number were tossed into the path of oncoming cavalry, each had a spike that was pointing upwards - with painful consequences.
4. What shape are the faces of a regular tetrahedron?

Answer: Equilateral triangles

Which explains why a tetrahedron is sometimes called a triangular pyramid. The tetrahedron is also seen in chemistry, in a myriad of covalent molecules, starting with CH4, methane - which has a carbon atom in the centre and four hydrogen atoms in the vertices of a regular tetrahedron.
5. The most familiar polyhedron is the regular hexahedron. What is the more common name of the regular hexahedron?

Answer: Cube

The cube has six faces, which are all squares, making it a regular hexahedron. It gives us the familiar six-sided dice, and numerous other common everyday objects. In chemistry, the cubic system is one of the most common shapes found in minerals - including crystals of sodium chloride.
6. The next regular polyhedron has eight triangular faces and twelve edges. What is it called?

Answer: Octahedron

The octahedron looks like two square-based pyramids with their bases stuck together. All the faces are equilateral triangles. It is found in nature as the form of crystals of fluorite or alum (you can easily grow crystals of potash alum to see this).
7. Mathematicians call the ten-sided die a pentagonal trapezohedron, which might be considered a bit strange because its faces are not pentagons. What shape are the ten faces of the pentagonal trapezohedron?

Answer: Kites

A pentagonal trapezohedron has ten congruent kite-shaped faces, five on top and five below, shifted so they fit together. It's called a pentagonal trapezohedron because it's the dual polyhedron to the pentagonal antiprism. (And what that means is far easier explained with diagrams - so feel free to look it up!)
8. The dodecahedron has twelve faces. What shape are the faces of the regular dodecahedron?

Answer: Pentagons

The dodecahedron has twelve pentagonal faces, and twenty vertices. Not that you're likely to come across this one outside of a set of polyhedral dice (where it is the D12), playing with a Megaminx - a dodecahedral version of the Rubik's Cube, or a model in a Mathematics classroom! A few quasi-crystals form this shape.
9. The last of the regular polyhedra has twenty faces, all of them equilateral triangles. What is it called?

Answer: Icosahedron

The icosahedron gets its name from the Greek "eikosi" which means twenty. The icosahedron turns up in nature - the herpes virus is an icosahedron, as are some of the amoeboid protozoa called Radiolarians. In gaming, besides being the shape of the iconic D20 polyhedral die, it is also the die used in Scattergories to choose one of twenty letters of the alphabet.
10. There are in fact only five convex polyhedra that are also regular, all their faces being regular polygons of the same size. They are named for a Greek philosopher. What are they called?

Answer: Platonic solids

Plato wrote about the five Platonic solids in his dialogue "Timaeus" in which he linked four of the five platonic solids with the four classical elements. The solid cube was earth; the tetrahedron with its upward point was fire; the octahedron was air; the icosahedron that rolls so easily was water; and the dodecahedron with its twelve faces (like the twelve signs of the zodiac) was the fifth element - "used for arranging the constellations on the whole heaven".
Source: Author Flamis

This quiz was reviewed by FunTrivia editor crisw before going online.
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